Equiangular lines in Euclidean spaces: Dimensions 17 and 18

Greaves, Gary; Syatriadi, Jeven; Yatsyna, Pavlo

doi:10.1090/mcom/3832

Equiangular lines in Euclidean spaces: Dimensions 17 and 18
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by Gary R. W. Greaves, Jeven Syatriadi and Pavlo Yatsyna;

Math. Comp. 92 (2023), 1867-1903

DOI: https://doi.org/10.1090/mcom/3832

Published electronically: March 8, 2023

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Abstract:

We show that the maximum cardinality of an equiangular line system in 17 dimensions is 48, thereby solving a longstanding open problem. Furthermore, by giving an explicit construction, we improve the lower bound on the maximum cardinality of an equiangular line system in 18 dimensions to 57.

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